We've been talking about increasing the series resistance for the coil driver path for the test masses. One consequence of this will be that we have reduced actuation range.

This may not be a big deal since for almost all of the LSC loops, we currently operate with a limiter on the output of the control filter bank. The value of the limit varies, but to get an idea of what sort of "threshold" velocities we are looking at, I calculated this for our Finesse 400 arm cavities. The calculation is rather simplistic (see Attachment #1), but I think we can still draw some useful conclusions from it:

• In Attachment #1, I've indicated with dashed vertical lines some series resistances that are either currently in use, or are values we are considering.
• The table below tabulates the fraction of passages through a resonance we will be able to catch, assuming velocities sampled from a Gaussian with width ~3um/s, which a recent ALS study suggests describes our SOS optic velocity distribution pretty well (with lcoal damping on).
• I've assumed that the maximum DAC output voltage available for length control is 8V.
• Presumably, this Gaussian velocity distribution will be modified because of the LSC actuation exerting impulses on the optic on failed attempts to catch lock. I don't have a good model right now for how this modification will look like, but I have some ideas.
• It would be interesting to compare the computed success rates below with what is actually observed.
• The implications of different series resistances on DAC noise are computed here (although the non-linear nature of the DAC noise has not been taken into account).

So, from this rough calculation, it seems like we would lose ~25% efficiency in locking the arm cavity if we up the series resistance from 400ohm to 1kohm. Doesn't seem like a big deal, becuase currently, the single arm locking